22. Doomsday or Extinction Suppose the population model (4) is modified to be dP dt = P(bP - a). (a) If a > 0, b > 0 show by means of a phase portrait (see An Autonomous DE ) that, depending on the initial condition P(0) = Po , the mathematical model could include a doomsday scenario (P(t) - co) or an extinction scenario (P(t) - 0) . (b) Solve the initial-value problem dP dt P(0.0005P - 0.1), P(0) = 300. Show that this model predicts a doomsday for the population in a finite time . (c) Solve the differential equation in part (b) subject to the initial condition P(0) = 100 . Show that this model predicts extinction for the population as too